The New CFS Divisia Monetary Aggregates: Design, Construction, and Data Sources

Abstract

The Center for Financial Stability (CFS) has initiated a new Divisia monetary aggregates database, maintained within the CFS program called Advances in Monetary and Financial Measurement (AMFM). The Director of the program is William A. Barnett, who is the originator of Divisia monetary aggregation and more broadly of the associated field of aggregation-theoretic monetary aggregation. The international section of the AMFM web site is a centralized source for Divisia monetary aggregates data and research for over 40 countries throughout the world. The components of the CFS Divisia monetary aggregates for the United States reflect closely those of the current and former simple-sum monetary aggregates provided by the Federal Reserve. The first five levels, M1, M2, M2M, MZM, and ALL, are composed of currency, deposit accounts, and money market accounts. The liquid asset extensions to M3, M4-, and M4 resemble in spirit the now discontinued M3 and L aggregates, including repurchase agreements, large denomination time deposits, commercial paper, and Treasury bills. When the Federal Reserve discontinued publishing M3 and L, the Fed stopped providing the consolidated, seasonally adjusted components. Also the Fed no longer provides the interest rates on the components. With so much of the needed component quantity and interest-rate data no longer available from the Federal Reserve, decisions about data sources needed in construction of the CFS aggregates have been far from easy and sometimes required regression interpolation. This paper documents the decisions of the CFS regarding United States data sources at the present time, with particular emphasis on Divisia M3 and M4.

Appendix: Regression Estimates for Broad-Aggregate Component Levels and Rates

For the broad-aggregate components not all data were available from a single source survey, or in some cases were not available at all for historical values. These levels and interest rates are estimated to fit with the current resources. In all cases a simple linear regression without a constant was used to approximate the past values. These estimations are used in the case of component levels for large denomination time deposits, levels of commercial paper, and levels and rates of repurchase agreements.

Because of the lack of data or the use of two distinct surveys for repo asset levels and interest rates, the past values of the components are estimated using a growth rate method of back calculation. A simple linear regression estimate was taken as well, but the splice produced large jumps at the point in time the series were linked.¹⁹ To avoid this jump, the growth rate method is used for the levels of repos instead. For the linear regression estimate, the values of the estimated survey are about 2.97 times those of the original, while the values for the growth rate method are 2.51 times the original levels. NYREPO _t is the level of repos from the New York Fed’s Primary Dealer Statistics survey, and RPNS _t is the monthly overnight and term RPs for commercial banks, available but discontinued on FRED. As previously mentioned, these two surveys are different, since NYREPO _t takes values for all primary dealers (banks, securities), while RPNS _t is described in FRED as only surveying commercial bank deals. The monthly growth rates for each series were calculated, DNYREPO _t and DRPNS _t , where D is the percentage growth rate operator. The growth rates from the FRED series are preserved for the months before October 2001, and then used to back calculate the levels from the initial level of the Primary Dealer Survey. For T, the time of the splice (October 2001), the initial Primary Dealer Survey is used to estimate the last value for repo levels available on FRED:

$$ NYR\widehat{E}P{O_{T - 1}} = \frac{{NYREP{O_T}}}{{\left( {1 + DRPN{S_{T - 1}}} \right)}} . $$

For all the preceding time periods, 0 ⩽ s ⩽ T − 2, the levels were estimated following the back calculation pattern and the available levels from the FRED survey:

$$ NYR\widehat{E}P{O_s} = \frac{{RPN{S_{s + 1}}}}{{\left( {1 + DRPN{S_s}} \right)}} . $$

The values for interest rates of repos were not available before 1995, and there was no comparable survey of repo rates from which to estimate. The available repo rates after 1995 were compared graphically to other interest rates, and the T-Bill rate was found to be the closest approximation and most useful, since it is available back to 1967 without any significant splices or changes of survey. Another linear regression without a constant was taken to determine the coefficient for the past values of the I-Repo interest rate index:

$$ IREP{O_t} = {\beta_r}*TB3M{S_t}, $$

where IREPO _t is the IREPO Index, β _r is the coefficient of the interest rate, and TB3MS _t is the 3-month Treasury bill secondary market (monthly) rate from FRED. For the overlapping period from November 1996 to December 2011, β _r was estimated, and the past values of the repo interest rate were then determined by:

$$ IR\widehat{E}P{O_t}= {\widehat{\beta}_r}*TB3M{S_t}. $$

In addition to estimating repo levels and rates, we spliced the levels for large denomination time deposits and commercial paper to compensate for their collection by two different surveys. The splice again uses a simple linear regression, and estimates the coefficient of the levels between the two surveys without intercept. For commercial paper, both asset level surveys are available from the Federal Reserve Board Statistics website under “Commercial Paper”.²⁰ The first survey is the “old structure” survey and runs to March of 2006. The “new structure” survey begins in January 2001. For the simple regression, NSCP _t is the new structure commercial paper values, while OSCP _t are the old structure commercial paper values. For the overlapping time period, β _CP is estimated by ${\widehat{\beta}_{CP}}$ and used to model the new survey values before January of 1991, as follows:

$$ \matrix{ {NSC{P_t} = {\beta_{CP}}*OSC{P_t}} \\ {N\widehat{S}C{P_t} = {{\widehat{\beta }}_{CP}}*OSC{P_t}.} \\ }<!end array> $$

Large denomination time deposits face a similar two-survey problem, requiring a splice. Again the same simple linear regression method is used to join the two surveys together. The current values come from the H.8 Survey, available from the Federal Reserve Board Statistics website. The previous values are provided by the FRED series, which were discontinued in March of 2006 along with other M3 components. Since the two series are different in their overlapping time periods, estimation was needed for those values before 1973. In 1973, the H.8 survey values are used outright, so the only estimation is for those values from 1967 to the end of 1972. The following equations relateLTDSL _t , which is FRED’s seasonally-adjusted monthly level of large time deposits from commercial banks, H8LTD _t , which is the value of large time deposits provided by the H.8 Survey, and ${\widehat{\beta}_{LTD}}$, which is the estimated value of the coefficient, β _LTD :

$$ \matrix{ {H8LT{D_t} = {\beta_{LTD}}*LTDS{L_t}} \\ {H8\widehat{L}T{D_t} = {{\widehat{\beta }}_{LTD}}*LTDS{L_t}} \\ }<!end array> $$

Table 3 is provided as a quick guide to these estimations. The table provides the sources, the overlapping time period used in the regressions, the time periods within which estimations were used, and the estimated values of the coefficients used to derive the past values.

Table 3 Regression estimates for broad aggregate components and rates